One of the challenges of understanding the complexity of so-called reform mathematics instruction lies in the observational tools used to capture it. This article introduces a unique tool, drawing from commognitive theory, for describing classroom discussions. The Realization Tree Assessment tool provides an image of a classroom discussion, depicting the realizations of the mathematical object manifested during the discussion and the narratives that articulate the links between these realizations. We applied the tool to 34 classroom discussions about a growing-pattern algebraic task and, through cluster analysis, found three types of whole-class discussion. Associations with classroom-level variables (track, but not grade level or teacher seniority) were also found. Implications with respect to applications and usefulness of the tool are discussed.
Merav Weingarden and Einat Heyd-Metzuyanim
David B. Custer and Ksenija Simic-Muller
We reflect on recent presentations at the NCTM annual conference and articles in MTLT that address statistics, data modeling, and data science. We observe that such presentations and articles are increasingly common, and encourage readers to use them in their teaching and write about their own adventures with data.
Kym Fry and Lyn D. English
Grade 4 students engage in problem solving through inquiry in an agricultural science context.
Margaret Rathouz, Nesrin Cengiz-Phillips, and Angela S. Krebs
Issues of equity in mathematics classrooms existed prior to COVID-19. For many students, however, meaningful participation in mathematical discussions became nearly impossible in online settings during the pandemic. In this study, we note the diversity in and nature of participation in mathematical discourse in an online course for preservice teachers (PSTs). We investigate the influence of implementing two support strategies for discussion: (a) establishing a “rough-draft/revision” orientation to mathematical tasks; and (b) providing time and structure (tasks and prompts) in an online discussion board for PSTs to post their initial thoughts, react to peers’ solutions, and collectively revise their ideas. In this article, we highlight several benefits of these support strategies to equitable PST participation in a unit on number theory. For example, as compared with oral discussions where only a few PSTs offered their ideas, the written discussion format encouraged every PST to post their ideas. Using a rough-draft/revision stance in the prompts fostered sharing and revealed diverse mathematical approaches, perspectives, and ideas. We argue that giving students opportunities to interact with one another and the mathematics in a variety of ways promotes equitable participation.
Blake E. Peterson, Douglas L. Corey, Benjamin M. Lewis, Jared Bukarau, and Introduction by: Wendy Cleaves
From the Archives highlights articles from NCTM’s legacy journals, previously discussed by the MTLT Journal Club.
Kathryn Early, K. Elizabeth Hammonds, Brea Ratliff, Mariya Rosenhammer, and W. Gary Martin
A high-leverage strategy first discussed more than 50 years ago, wait time has many benefits for both teachers and students yet is not used to its full potential. See how it can enhance your students’ mathematical discourse.
This department provides a space for current and past PK-12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.
Ethan P. Smith, Jennifer Kelly, Susan Sappington, Kareemah Warren, and Amanda Jansen
Language is a conduit for communicating and understanding mathematical ideas. This article explores how we can use judicious telling to attend to students’ written and spoken literacy in mathematics.
Stephanie D. Sigmon, Kelly Q. Halpin, Damien J. Ettere, and Jennifer Suh
This article models how to plan and facilitate implementing the same task in two sixth-grade classrooms with two different learning goals using the Five Practices structure.
Ashley Schmidt, Treshonda Rutledge, Tandrea Fulton, and Sarah B. Bush
Do you use mathematical discussions to increase engagement in your classroom? In this Front and Center article, authors provide a discourse tool that can be used to reveal potential biases found in the implementation of the Five Practices.